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2) Assume that we had an equation of the form Ax? + Bxy + Cy? +Dx...
Now consider the conic represented by the equation xyy-22x +2/2y-0. For this equation, it is more...
conic section
Now consider the conic represented by the equation xyy-22x +2/2y-0. For this equation, it is more difficult to wrte t in the form -h. 1 because of the xyterm. When a conic with equaticon difficult to write it in the formk - 1 because of the xy term. When a conic with equation ax' + bxy + cy'+dx ey+-0 is rotated about an angle 6, where cot 20-converting from basis B: # {( 1, 0), (0, 1)) to...
2. (15) Give the standard form equation of the parabola with vertex = (1,2) and focus = (3, 2) b....
2. (15) Give the standard form equation of the parabola with vertex = (1,2) and focus = (3, 2) b. the ellipse with center (-1,3), a focus at (-1,7) and a major axis point (1,8) c. the hyperbola with foci at (3,3), (3,-7) and vertices at (3,1), (3,-5). 3. (12) Identify the conic section and complete the square to give the standard equation given 3x2-10y +36x -20y+38 0 is 3 (24) Given the parametric equations x-Y-2, y-t,-2 4· a. Sketch...
Suppose an indifference curve is given by the equation U=2*C*T. Assume that initially the consumer owns...
Suppose an indifference curve is given by the equation U=2*C*T. Assume that initially the consumer owns the bundle C = 20, T = 2. What is the Utility value along this indifference curve? Show your calculations! Other than point, (C, T) = (20, 2), list 3 other points on this indifference curve. Graph the indifference curve including the point (C, T) = (20, 2) and the 3 points you listed in part b. Place T on the vertical axis and...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t))...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
2 photos but they are the one question If a curve whose polar equation is r...
2 photos but they are the one question
If a curve whose polar equation is r = f() is rotated about the pole though an angle $, then an equation for the rotated curve is r = f(-6). write an equation for the limaçon r = 3 - sin after it has been rotated counterclockwise by the given amount. Use a graphing utility to graph the rotated limaçon for 8 = 7/4, e = 7/2, 8-, and 0 = 3/2....
17. Consider the differential equation given by dy/dx = xy/2
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
2-5 1. Find the Domain of the function and identify any asymptotes (6 pts.) 3. Find...
2-5
1. Find the Domain of the function and identify any asymptotes (6 pts.) 3. Find the equation of an ellipse with vertices (0, 2) and (8, 2) and a minor axis length of length 6. (3 pts.) (@ y"3x - 1 (6) S(x)- (c) "(x)=-**-***10 4. Graph the conic and identify the type of conic, the center, vertices, and foci, if applicable.(8 pts.) (9251 2. Identify any x-intercepts; y-intercepts and asymptotes of the graph of the function. Then sketch...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d =...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Iry to hhel ieal 4 Suppose that the 3 x 2 matrix A has rank 2 and we want to solve Ax b. a) (10 pts) If there ex...
Iry to hhel ieal 4 Suppose that the 3 x 2 matrix A has rank 2 and we want to solve Ax b. a) (10 pts) If there exists a solution x ()l show that 0 0 b) (5 pts) Is the 3 x 3 augmented matrix (Alb) invertible? Why or why not? c) (10 pts) Suppose that you found the solution below 2 (A | b) 30 0 Can you compute the solution to Ax = b? If yes...
conic section
Now consider the conic represented by the equation xyy-22x +2/2y-0. For this equation, it is more difficult to wrte t in the form -h. 1 because of the xyterm. When a conic with equaticon difficult to write it in the formk - 1 because of the xy term. When a conic with equation ax' + bxy + cy'+dx ey+-0 is rotated about an angle 6, where cot 20-converting from basis B: # {( 1, 0), (0, 1)) to...
2. (15) Give the standard form equation of the parabola with vertex = (1,2) and focus = (3, 2) b. the ellipse with center (-1,3), a focus at (-1,7) and a major axis point (1,8) c. the hyperbola with foci at (3,3), (3,-7) and vertices at (3,1), (3,-5). 3. (12) Identify the conic section and complete the square to give the standard equation given 3x2-10y +36x -20y+38 0 is 3 (24) Given the parametric equations x-Y-2, y-t,-2 4· a. Sketch...
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
you can skip question 1
Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
2 photos but they are the one question
If a curve whose polar equation is r = f() is rotated about the pole though an angle $, then an equation for the rotated curve is r = f(-6). write an equation for the limaçon r = 3 - sin after it has been rotated counterclockwise by the given amount. Use a graphing utility to graph the rotated limaçon for 8 = 7/4, e = 7/2, 8-, and 0 = 3/2....
2-5
1. Find the Domain of the function and identify any asymptotes (6 pts.) 3. Find the equation of an ellipse with vertices (0, 2) and (8, 2) and a minor axis length of length 6. (3 pts.) (@ y"3x - 1 (6) S(x)- (c) "(x)=-**-***10 4. Graph the conic and identify the type of conic, the center, vertices, and foci, if applicable.(8 pts.) (9251 2. Identify any x-intercepts; y-intercepts and asymptotes of the graph of the function. Then sketch...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Iry to hhel ieal 4 Suppose that the 3 x 2 matrix A has rank 2 and we want to solve Ax b. a) (10 pts) If there exists a solution x ()l show that 0 0 b) (5 pts) Is the 3 x 3 augmented matrix (Alb) invertible? Why or why not? c) (10 pts) Suppose that you found the solution below 2 (A | b) 30 0 Can you compute the solution to Ax = b? If yes...
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